Theorems · Theorem · field theory
NNRat.smul_def
∀ {K : Type u_1} [inst : DivisionSemiring K] (q : ℚ≥0) (a : K), q • a = ↑q * a- Defined in
- Mathlib.Algebra.Field.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRatstatement and proof · cited by 523
- NNRat.caststatement · cited by 235
- DivisionSemiringstatement and proof · cited by 216
- DivisionSemiring.nnqsmul_defproof · cited by 1
Cited by7
Results whose statement or proof uses this declaration.
- NNRat.smul_one_eq_castproof · cited by 2
- Finset.expect_eq_sum_div_cardproof · cited by 2
- Finset.expect_boole_mulproof · cited by 1
- SubfieldClass.nnqsmul_memproof · cited by 0
- Finset.expect_indicator_oneproof · cited by 0
- Complex.ofReal_nnqsmulproof · cited by 0
- nnqsmul_nonnegproof · cited by 0